Linear control techniques are the foundation of control system design and analysis. Control System Toolbox™ lets you create and manipulate the linear models of your control system.
All standard model representations are supported, including transfer function, zero-pole-gain, explicit and descriptor state-space, and frequency-response data. Linear models can be SISO or MIMO, and continuous or discrete. You can represent PID controllers as PID objects. In addition, you can accurately model and simulate systems with time delays, including feedback loops with delays.
Control System Toolbox enables you to create and work with collections of linear models and model arrays. You can use model arrays to represent and analyze sensitivity to parameter variations or to validate a controller design against several plant models. You can also approximate nonlinear dynamics using linear parameter-varying (LPV) systems. The toolbox lets you simulate such systems using LPV System block.
Building a model of your plant is usually the first step in designing a control system. If no linear model is available, you can build one by fitting test data using System Identification Toolbox™, or by linearizing a Simulink® model using Simulink Control Design™. Once you have created a linear model, you can use Control System Toolbox to analyze it and design a controller.
Control System Toolbox provides commands for:
Control System Toolbox provides an app and functions for computing low-order approximations of high-order models. Using the Model Reducer app, you can simplify high-order linear models while preserving model dynamics that are important to your application. You can remove states with low energy contributions, select significant modes, and cancel close pole/zero pairs. You can also compare the original and reduced models using time and frequency domain plots.
Control System Toolbox provides an app and functions for analyzing linear models. Using the Linear System Analyzer app, you can view and compare the time and frequency responses of several linear models at once. You can also inspect key performance parameters, such as rise time, settling time, maximum overshoot, and stability margins. Available plots include step response, impulse response, Bode, Nichols, Nyquist, singular value, and zero-pole. You can simulate the response to user-defined inputs and initial conditions to further investigate system performance.
Control System Toolbox lets you systematically tune control system parameters using SISO and MIMO design techniques. You can also design Kalman filters.
If a linear model of the plant is not available, you can identify a plant model from measured input-output data directly in the PID Tuner app using System Identification Toolbox.
The Control System Designer app lets you design and analyze SISO control systems. You can:
In addition to standard model representations, such as transfer function and frequency-response data, the Control System Designer app supports systems with time delays. You can also work with several plant models simultaneously to evaluate your control design for different operating conditions.
Simulink Control Design extends Control System Toolbox by enabling you to tune controllers in Simulink that consist of several SISO loops. You can close SISO loops sequentially, visualize loop interactions, and iteratively tune each loop for best overall performance. Simulink Control Design lets you export the tuned parameters directly to Simulink for further design validation through nonlinear simulation.
When used with Simulink Design Optimization™, the Control System Designer app lets you optimize the control system parameters to enforce time-based and frequency-based performance requirements. When used with Robust Control Toolbox, the app lets you automatically shape open-loop responses using H-infinity algorithms.
Most embedded control systems have a fixed architecture with simple tunable elements such as gains, PID controllers, or low-order filters. Such architectures are easier to understand, implement, schedule, and retune than complex centralized controllers. Control System Toolbox provides functions and the Control System Tuner app for modeling and tuning these decentralized control architectures. You can:
The toolbox also lets you tune one controller against a set of plant models. This enables you to design a controller that will be robust to changes in plant dynamics due to variations in operating conditions, and also able to sensor or actuator failures.
Gain scheduling is a linear technique used for controlling nonlinear or time-varying plants. This technique involves computing linear approximations of the plant at various operating conditions, tuning controller gains at the operating condition, and scheduling controller gains as the plant changes operating conditions. Control System Toolbox provides tools for automatically computing gain schedules for fixed-structure control systems. You can: